'Anyons' Could Blur the Boson-Fermion Gap

Any student of particle physics can tell you that all subatomic particles in Nature fall into two distinct classes: fermions (electrons, neutrons, protons, etc.) and bosons (photons and other force-carrying “messenger” particles).

Back in 1982, however, physicist Frank Wilczek and several of his colleagues proposed that — theoretically, at least — there could be particles that exist between those two discrete classes.

Wilczek dubbed them “anyons” because any anyon can be anything between a boson and a fermion. “Wilczek is a funny guy,” Tassilo Keilmann told Symmetry Breaking. Keilmann is a physicist at Munich’s Ludwig Maximilian University, and he’s designed an experiment he thinks will bring anyons into the realm of the observable world, using cold atoms and lasers — and a smidgen of ingenuity.

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The whole notion of anyons is bizarre, if you think about it. I mean, quantum field theory — the marriage of quantum mechanics with special relativity — dictates that there are only two discrete possibilities for classes of particles: bosons and fermions. The existence of anyons should be ruled out by the quantum mechanical playbook. So what gives?

Chillin’ at the Subatomic Cafe

Imagine you are a humble electron, and you walk into the Subatomic Cafe for a nice big bowl of quark soup. The room is filled with elementary particles, both bosons and your fellow fermions. Where do you sit?

Electrons are restless particles with serious intimacy issues; they need a lot of personal space. Each electron in the cafe occupies only one seat at a given table, and would shove off a stranger who tried to sit in his or her lap –- although if that person happened to be an attractive member of the opposite sex, the two could share a table.

The tables, each with a certain number of seats, represent specific energy states. Only a certain number of electrons can occupy a given state. For instance, a helium atom has two electrons, and both can occupy the same “seat” provided they are opposite “genders,” determined by a mysterious property called “spin” (i.e., one is spin up, the other is spin down). In this case, two is company, and three is definitely a crowd: if a third electron tries to horn in, it will be bumped up to the next energy level.

As an atom absorbs energy and new electrons are added, the electrons fill up the “seats” one by one, beginning with the most desirable “table” — the ground state — and working outward. This is the Pauli exclusion principle: once an electron occupies a seat, it excludes others like itself from sitting in the same seat. (There is no lap dancing in electron land.)

Bosons, in contrast, have serious boundary issues; lap dances are de rigeur. They love to crowd together in the same space. Why, they’d turn the entire Subatomic Cafe into one giant mosh pit given half a chance! You and the other fermions click your tongues in disapproval at the grotesque lack of disciplined order on display.

But at least everyone knows their place, and sticks with their own kind. The Subatomic Cafe is unapologetically segregated in that respect. Anyons upset the rigid quantum social order; they refuse to choose a side. They can do that because — at least to date — they only “exist” in two dimensions. That’s right, the Subatomic Cafe happens to be part of the proverbial Flatland.

It might seem silly to talk of two dimensions, since we occupy three-dimensional space (and a fourth dimension of time). As Wilczek explained to Science Watch back in 1991:

Experimentalists can make substances — as can nature, for that matter — that are very planar in their structure. Graphite is a good example. It’s very easy for electrons in graphite to move within a plane, but difficult for them to jump between planes…. Therefore, inhabitants of that plane effectively live in a two-dimensional world.

So yes, physicists can create two-dimensional systems in the lab. And two-dimensional worlds play by their own rules. “Fermions and bosons are the only possibility if the dimension of space is three or more,” Wilczek explained back in 1991. “If the dimension of space is two, however, then there is a continuous range of possibilities, and those are the anyons.”

Consider an Optical Egg Crate

This is where Keilmann comes in. We now have the tools to create “artificial particles” in the lab, and manipulate them individually, albeit at ultracold temperatures (on the order of 10-10 kelvin). This enables scientists to study the strange, small world of quantum physics as if they were looking at it through a magnifying glass.

Keilmann proposes building a grid of lasers known as an optical lattice, and then introducing a cloud of boson rubidium 87 chilled to ultracold temperatures. Those particles should settle into the spaces between the laser boundaries, much like eggs settle into an egg crate. Per Symmetry Breaking:

The idea is to set up the optical egg crate with some prescribed boson arrangement, use a laser to give them some energy, and watch to see which of them hop from their own well to a different well. The energy they’re given isn’t enough to hop over the energy boundary by the laser, which means they’ll have to tunnel through the barrier to get to another site. In quantum mechanical systems, tunneling happens on occasion, and it’s no big deal. But tunneling doesn’t usually depend on what’s on the other side of the barrier.Once excited by a laser, the boson may hop to an empty well, or it may hop to one that’s already occupied, and will lose some energy as it tunnels. If the theory bears out, the chances of a boson hopping to another site and the amount of energy it has post-hop will depend on the occupancy of that site. That means that you can reasonably predict whether it will congregate or isolate through this conditional hopping.

Keilmann calls this “conditional hopping.” Translation: if the bosons start acting more like fermions, avoiding certain wells in the egg crate much like fermions avoid other fermions with the same spin state, then those rigid class boundaries aren’t as rigid after all. They would technically be anyons, straddling the gap between bosons and fermions, bringing desegregation to the quantum world.